Chaos in fractional-order difference systems

To follow up on the progress made on exploring the stability investigation of linear commensurate Fractional-order Difference Systems (FoDSs), such topic of its extended version that appears with incommensurate orders is discussed and examined in this work. Some simple applicable conditions for judging the stability of these systems are reported as novel results. These results are formulated by converting the linear incommensurate FoDS into another equivalent system consists of fractional-order difference equations of Volterra convolution-type as well as by using some properties of the Z-transform method. All results of this work are verified numerically by illustrating some examples that deal with the stability of solutions of such systems.

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Novel convenient conditions for the stability of nonlinear incommensurate fractional-order difference systems

Alexandria Engineering Journal ◽

10.1016/j.aej.2021.06.073 ◽

2021 ◽

Author(s):

Mohd Taib Shatnawi ◽

Noureddine Djenina ◽

Adel Ouannas ◽

Iqbal M. Batiha ◽

Giuseppe Grassi

Keyword(s):

Fractional Order ◽

Order Difference ◽

Difference Systems ◽

The Stability

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On Mittag–Leffler Stability of Fractional Order Difference Systems

Lecture Notes in Electrical Engineering - Advances in Modelling and Control of Non-integer-Order Systems ◽

10.1007/978-3-319-09900-2_19 ◽

2015 ◽

pp. 209-220 ◽

Cited By ~ 2

Author(s):

Małgorzata Wyrwas ◽

Dorota Mozyrska

Keyword(s):

Fractional Order ◽

Order Difference ◽

Difference Systems

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Chaos in the discrete memristor-based system with fractional-order difference

Results in Physics ◽

10.1016/j.rinp.2021.104106 ◽

2021 ◽

Vol 24 ◽

pp. 104106

Author(s):

Yuexi Peng ◽

Shaobo He ◽

Kehui Sun

Keyword(s):

Fractional Order ◽

Order Difference

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Oscillation Results for a Class of Nonlinear Fractional Order Difference Equations with Damping Term

Journal of Function Spaces ◽

10.1155/2020/5495873 ◽

2020 ◽

Vol 2020 ◽

pp. 1-10

Author(s):

A. George Maria Selvam ◽

Jehad Alzabut ◽

Mary Jacintha ◽

Abdullah Özbekler

Keyword(s):

Fractional Order ◽

Difference Equations ◽

Difference Operator ◽

Fractional Operators ◽

Damping Term ◽

Fractional Difference ◽

Riccati Technique ◽

Order Difference ◽

Numerical Examples ◽

Positive Integers

The paper studies the oscillation of a class of nonlinear fractional order difference equations with damping term of the form Δψλzηλ+pλzηλ+qλF∑s=λ0λ−1+μ λ−s−1−μys=0, where zλ=aλ+bλΔμyλ, Δμ stands for the fractional difference operator in Riemann-Liouville settings and of order μ, 0<μ≤1, and η≥1 is a quotient of odd positive integers and λ∈ℕλ0+1−μ. New oscillation results are established by the help of certain inequalities, features of fractional operators, and the generalized Riccati technique. We verify the theoretical outcomes by presenting two numerical examples.

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Fractional-Order SIR Epidemic Model for Transmission Prediction of COVID-19 Disease

Applied Sciences ◽

10.3390/app10238316 ◽

2020 ◽

Vol 10 (23) ◽

pp. 8316

Author(s):

Kamil Kozioł ◽

Rafał Stanisławski ◽

Grzegorz Bialic

Keyword(s):

Fractional Order ◽

Epidemic Model ◽

Dynamic Properties ◽

Sir Model ◽

Domain Model ◽

Sir Epidemic Model ◽

Step Method ◽

Order Difference ◽

Sir Epidemic ◽

The Time Domain

In this paper, the fractional-order generalization of the susceptible-infected-recovered (SIR) epidemic model for predicting the spread of the COVID-19 disease is presented. The time-domain model implementation is based on the fixed-step method using the nabla fractional-order difference defined by Grünwald-Letnikov formula. We study the influence of fractional order values on the dynamic properties of the proposed fractional-order SIR model. In modeling the COVID-19 transmission, the model’s parameters are estimated while using the genetic algorithm. The model prediction results for the spread of COVID-19 in Italy and Spain confirm the usefulness of the introduced methodology.

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